Re: Phantom Roll: Knowing the Odds (long, math)

This is a reasonably simple explanation to the theory behind dice probability, and much of the myth and superstition behind it:

http://mathforum.org/library/drmath/view/56502.html

What Karinya and I did above was simply extend the concept of rolling dice to keep adding one die at a time until specific conditions were reached. Karinya used a statistical model, I used iterative programming, and we basically arrived at roughly the same conclusion - two paths to the same general goal.

Karinya basically took the concept of a single die roll: one value determined randomly between 1 and 6, then used a spreadsheet to create an expanded chart of the results of various additional rolls, then did some manipulation to the final results to get percentages.

My method used a program that simulates dice rolls, then sets conditions under which the rolling stops - the program then keeps rolling dice until it fulfills one of my terminating conditions, then records the result for tabulation at the end. It repeats this process one million times, then examines the frequency of each result.

Karinya's method is numerically accurate, but underlying math and conditions become increasingly complex as you start adding more conditions to the experiment. My method is less accurate, but is more tolerant of new test conditions.

To learn more about statistics, you'll probably need to take a formal course either in high school or college. It's possible to learn statistics from the web, but I don't recommend it; it's very easy to get confused and misunderstand many of the concepts behind probability and statistics.

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As I mention above, I can easily add weighting to my program, but I need some reliable numbers to generate a valid weighting scheme.

Icemage

Originally posted by

**IfritnoItazura**http://mathforum.org/library/drmath/view/56502.html

What Karinya and I did above was simply extend the concept of rolling dice to keep adding one die at a time until specific conditions were reached. Karinya used a statistical model, I used iterative programming, and we basically arrived at roughly the same conclusion - two paths to the same general goal.

Karinya basically took the concept of a single die roll: one value determined randomly between 1 and 6, then used a spreadsheet to create an expanded chart of the results of various additional rolls, then did some manipulation to the final results to get percentages.

My method used a program that simulates dice rolls, then sets conditions under which the rolling stops - the program then keeps rolling dice until it fulfills one of my terminating conditions, then records the result for tabulation at the end. It repeats this process one million times, then examines the frequency of each result.

Karinya's method is numerically accurate, but underlying math and conditions become increasingly complex as you start adding more conditions to the experiment. My method is less accurate, but is more tolerant of new test conditions.

To learn more about statistics, you'll probably need to take a formal course either in high school or college. It's possible to learn statistics from the web, but I don't recommend it; it's very easy to get confused and misunderstand many of the concepts behind probability and statistics.

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Originally posted by

**Matera**Icemage

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